H₂ input load disturbance rejection controller design for synchronised output regulation of time-delayed multi-agent systems with frequency domain method

ABSTRACT

An analytical H ₂ input load disturbance rejection (ILDR) controller design approach is presented for the synchronised output regulation (SOR) of homogeneous time-delayed multi-agent systems. First, a closed-loop multi-input multi-output framework with transfer functions is introduced, and an SOR condition is given. Second, the decomposition method is utilised to simplify the analysis of internal stability and H ₂ performance index of the whole system to a set of independent optimisation problems with respect to the eigenvalues of the topology matrix. Finally, for each decomposed subsystem, the H ₂ optimal ILDR controller can be computed from all the stabilising controllers. By comparison with the conventional given-structured controllers, the contributions of the new approach are that the design procedure is calculated analytically for multi-agent systems with input disturbances, and a simple quantitative tuning way is developed to trade-off the nominal performance and robustness. The simulation example shows the effective ILDR capability of the proposed control strategy.

KEYWORDS:

• Synchronised output regulation
• multi-agent systems
• time delays
• H ₂ performance index
• frequency domain

Acknowledgments

This paper is partly supported by the National Science Foundation of China (61473183, U1509211). The authors would like to thank antonymous reviewers for their constructive suggestions and comments which improve substantially the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Natural Science Foundation of China [grant number 61473183], [grant number U1509211].